26,460 research outputs found
Pattern vectors from algebraic graph theory
Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs
A Framework for Symmetric Part Detection in Cluttered Scenes
The role of symmetry in computer vision has waxed and waned in importance
during the evolution of the field from its earliest days. At first figuring
prominently in support of bottom-up indexing, it fell out of favor as shape
gave way to appearance and recognition gave way to detection. With a strong
prior in the form of a target object, the role of the weaker priors offered by
perceptual grouping was greatly diminished. However, as the field returns to
the problem of recognition from a large database, the bottom-up recovery of the
parts that make up the objects in a cluttered scene is critical for their
recognition. The medial axis community has long exploited the ubiquitous
regularity of symmetry as a basis for the decomposition of a closed contour
into medial parts. However, today's recognition systems are faced with
cluttered scenes, and the assumption that a closed contour exists, i.e. that
figure-ground segmentation has been solved, renders much of the medial axis
community's work inapplicable. In this article, we review a computational
framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009,
2013), that bridges the representation power of the medial axis and the need to
recover and group an object's parts in a cluttered scene. Our framework is
rooted in the idea that a maximally inscribed disc, the building block of a
medial axis, can be modeled as a compact superpixel in the image. We evaluate
the method on images of cluttered scenes.Comment: 10 pages, 8 figure
The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch
Recent and forthcoming advances in instrumentation, and giant new surveys,
are creating astronomical data sets that are not amenable to the methods of
analysis familiar to astronomers. Traditional methods are often inadequate not
merely because of the size in bytes of the data sets, but also because of the
complexity of modern data sets. Mathematical limitations of familiar algorithms
and techniques in dealing with such data sets create a critical need for new
paradigms for the representation, analysis and scientific visualization (as
opposed to illustrative visualization) of heterogeneous, multiresolution data
across application domains. Some of the problems presented by the new data sets
have been addressed by other disciplines such as applied mathematics,
statistics and machine learning and have been utilized by other sciences such
as space-based geosciences. Unfortunately, valuable results pertaining to these
problems are mostly to be found only in publications outside of astronomy. Here
we offer brief overviews of a number of concepts, techniques and developments,
some "old" and some new. These are generally unknown to most of the
astronomical community, but are vital to the analysis and visualization of
complex datasets and images. In order for astronomers to take advantage of the
richness and complexity of the new era of data, and to be able to identify,
adopt, and apply new solutions, the astronomical community needs a certain
degree of awareness and understanding of the new concepts. One of the goals of
this paper is to help bridge the gap between applied mathematics, artificial
intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in
Astronomy, special issue "Robotic Astronomy
Disconnected Skeleton: Shape at its Absolute Scale
We present a new skeletal representation along with a matching framework to
address the deformable shape recognition problem. The disconnectedness arises
as a result of excessive regularization that we use to describe a shape at an
attainably coarse scale. Our motivation is to rely on the stable properties of
the shape instead of inaccurately measured secondary details. The new
representation does not suffer from the common instability problems of
traditional connected skeletons, and the matching process gives quite
successful results on a diverse database of 2D shapes. An important difference
of our approach from the conventional use of the skeleton is that we replace
the local coordinate frame with a global Euclidean frame supported by
additional mechanisms to handle articulations and local boundary deformations.
As a result, we can produce descriptions that are sensitive to any combination
of changes in scale, position, orientation and articulation, as well as
invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV:
Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In
ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape
Recognition. Masters thesis, Department of Computer Engineering, Middle East
Technical University, May 200
Multi-view Convolutional Neural Networks for 3D Shape Recognition
A longstanding question in computer vision concerns the representation of 3D
shapes for recognition: should 3D shapes be represented with descriptors
operating on their native 3D formats, such as voxel grid or polygon mesh, or
can they be effectively represented with view-based descriptors? We address
this question in the context of learning to recognize 3D shapes from a
collection of their rendered views on 2D images. We first present a standard
CNN architecture trained to recognize the shapes' rendered views independently
of each other, and show that a 3D shape can be recognized even from a single
view at an accuracy far higher than using state-of-the-art 3D shape
descriptors. Recognition rates further increase when multiple views of the
shapes are provided. In addition, we present a novel CNN architecture that
combines information from multiple views of a 3D shape into a single and
compact shape descriptor offering even better recognition performance. The same
architecture can be applied to accurately recognize human hand-drawn sketches
of shapes. We conclude that a collection of 2D views can be highly informative
for 3D shape recognition and is amenable to emerging CNN architectures and
their derivatives.Comment: v1: Initial version. v2: An updated ModelNet40 training/test split is
used; results with low-rank Mahalanobis metric learning are added. v3 (ICCV
2015): A second camera setup without the upright orientation assumption is
added; some accuracy and mAP numbers are changed slightly because a small
issue in mesh rendering related to specularities is fixe
Many-to-Many Graph Matching: a Continuous Relaxation Approach
Graphs provide an efficient tool for object representation in various
computer vision applications. Once graph-based representations are constructed,
an important question is how to compare graphs. This problem is often
formulated as a graph matching problem where one seeks a mapping between
vertices of two graphs which optimally aligns their structure. In the classical
formulation of graph matching, only one-to-one correspondences between vertices
are considered. However, in many applications, graphs cannot be matched
perfectly and it is more interesting to consider many-to-many correspondences
where clusters of vertices in one graph are matched to clusters of vertices in
the other graph. In this paper, we formulate the many-to-many graph matching
problem as a discrete optimization problem and propose an approximate algorithm
based on a continuous relaxation of the combinatorial problem. We compare our
method with other existing methods on several benchmark computer vision
datasets.Comment: 1
Correcting curvature-density effects in the Hamilton-Jacobi skeleton
The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method
Active skeleton for bacteria modeling
The investigation of spatio-temporal dynamics of bacterial cells and their
molecular components requires automated image analysis tools to track cell
shape properties and molecular component locations inside the cells. In the
study of bacteria aging, the molecular components of interest are protein
aggregates accumulated near bacteria boundaries. This particular location makes
very ambiguous the correspondence between aggregates and cells, since computing
accurately bacteria boundaries in phase-contrast time-lapse imaging is a
challenging task. This paper proposes an active skeleton formulation for
bacteria modeling which provides several advantages: an easy computation of
shape properties (perimeter, length, thickness, orientation), an improved
boundary accuracy in noisy images, and a natural bacteria-centered coordinate
system that permits the intrinsic location of molecular components inside the
cell. Starting from an initial skeleton estimate, the medial axis of the
bacterium is obtained by minimizing an energy function which incorporates
bacteria shape constraints. Experimental results on biological images and
comparative evaluation of the performances validate the proposed approach for
modeling cigar-shaped bacteria like Escherichia coli. The Image-J plugin of the
proposed method can be found online at http://fluobactracker.inrialpes.fr.Comment: Published in Computer Methods in Biomechanics and Biomedical
Engineering: Imaging and Visualizationto appear i
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